Annals of Glaciology 56(70) 2015 doi: 10.3189/2015AoG70A113
89
Simulations of changes to Glaciar Zongo, Bolivia (16° S),
over the 21st century using a 3-D full-Stokes model and
CMIP5 climate projections
Marion RÉVEILLET,1,2 Antoine RABATEL,1,2 Fabien GILLET-CHAULET,1,2
Alvaro SORUCO3
1
Laboratoire de Glaciologie et Géophysique de l’Environnement (LGGE), Université Grenoble Alpes, Grenoble, France
2
LGGE, CNRS, Grenoble, France
3
Instituto de Investigaciones Geológicas y del Medio Ambiente, Universidad Mayor de San Andrés, La Paz, Bolivia
Correspondence: Marion Réveillet <[email protected]>
ABSTRACT. Bolivian glaciers are an essential source of fresh water for the Altiplano, and any changes
they may undergo in the near future due to ongoing climate change are of particular concern. Glaciar
Zongo, Bolivia, located near the administrative capital La Paz, has been extensively monitored by the
GLACIOCLIM observatory in the last two decades. Here we model the glacier dynamics using the 3-D
full-Stokes model Elmer/Ice. The model was calibrated and validated over a recent period (1997–2010)
using four independent datasets: available observations of surface velocities and surface mass balance
were used for calibration, and changes in surface elevation and retreat of the glacier front were used for
validation. Over the validation period, model outputs are in good agreement with observations
(differences less than a small percentage). The future surface mass balance is assumed to depend on the
equilibrium-line altitude (ELA) and temperature changes through the sensitivity of ELA to temperature.
The model was then forced for the 21st century using temperature changes projected by nine Coupled
Model Intercomparison Project phase 5 (CMIP5) models. Here we give results for three different
representative concentration pathways (RCPs). The intermediate scenario RCP6.0 led to 69 � 7%
volume loss by 2100, while the two extreme scenarios, RCP2.6 and RCP8.5, led to 40 � 7% and
89 � 4% loss of volume, respectively.
KEYWORDS: glacier flow, glacier mass balance, mountain glaciers, tropical glaciology
1. INTRODUCTION
The Bolivian Cordillera Oriental contains more than 1800
glaciers, covering a total area of �450 km2 (Soruco, 2008).
Water resources from these glaciers are extremely important
for the Bolivian Altiplano, where the administrative capital,
La Paz, is located. Runoff from glaciers is an essential source
of fresh water for direct consumption by the inhabitants, as
well as for irrigation water for agriculture and water for the
generation of hydropower. Soruco (2008) and Soruco and
others (2015) determined that glacier meltwater contributes
�15% of the water resources of La Paz annually, and up to
27% in the dry season.
Several studies have shown that tropical glaciers are
particularly sensitive to climate change because tropical
climate conditions maintain the lower reaches of the
glaciers under ablation conditions all year round, so small
changes in temperature and precipitation can have a major
impact on their mass balance (Francou and others, 2003;
Vuille and others, 2008; Rabatel and others, 2013). All
glaciers in the tropical Andes have retreated significantly
since the Little Ice Age maximum (Rabatel and others, 2008;
Jomelli and others, 2009). In a recent review of glaciological
surveys in the tropical Andes, Rabatel and others (2013)
showed that in recent decades glacier shrinkage has
accelerated with changing climate conditions and particularly with increasing temperatures. In this context, the
question of the future of glaciers in the Andes, particularly in
the Bolivian cordilleras, is extremely important for scientists
and society.
A wide range of future climate projections for the next
century, under different forcing scenarios derived from
different climate models, is available from the Coupled
Model Intercomparison Project phase 5 (CMIP5) (http://
www.cmip-pcmdi.llnl.gov). These climate model results
provide a solid basis for studying the response of glaciers
to ongoing climate change.
To quantify future changes in glacier volume, the surface
mass balance needs to be estimated, and ice dynamics have
to be accounted for by transferring mass from accumulation
to ablation zones. Approaches used to estimate mass
balances in previous studies range from the sensitivity of
the mass balance to temperature (e.g. Vincent and others,
2014) to the spatial distribution of surface mass balance
calculated using a model driven by climate variables (e.g.
Huss and others, 2010), despite considerable climateforcing uncertainties. We preferred to use a simple approach
to parameterize changes to the surface mass balance. In
tropical conditions, sublimation is too significant to use a
simple degree-day model (Sicart and others, 2008), and the
use of a full surface energy-balance model remains
questionable because some of the input parameters are
not accurately reproduced by the climate models. Different
approaches to ice dynamics have been used in previous
studies on mountain glaciers. Empirical approaches do not
aim to reproduce glacier dynamics and fluctuations with
high precision or in great detail and can thus rely on
parameterization of varying complexity (Oerlemans and
others, 1998; Vincent and others, 2000, 2014; Sugiyama
90
and others, 2007; Huss and others, 2010; Carlson and
others, 2014). Physical approaches rely on the use of
numerical ice-flow models to solve the equations describing
the flow of ice. Numerous ice-flow models of varying
degrees of complexity have been developed and applied to
both real and synthetic situations (Bindschadler, 1982;
Hubbard and others, 1998; Le Meur and Vincent, 2003;
Schäfer and Le Meur, 2007; Gudmundsson, 1999; Le Meur
and others, 2007; Jouvet and others, 2008). One drawback
of these approaches is that they require a large number of in
situ observations to calibrate and validate the model.
In the present study, we used a physical approach. Thanks
to the increase in computational power, solving the full set of
mechanical equations that govern the flow of ice in glaciers
or ice sheets without approximations (i.e. the full-Stokes
equations) does not limit potential applications. Here we use
the 3-D full-Stokes ice-flow model Elmer/Ice (Gagliardini
and others, 2013) for an application on a mountain glacier in
the tropical Andes, i.e. Glaciar Zongo, Bolivia.
Glaciar Zongo is a part of the GLACIOCLIM observatory
(http://www-lgge.ujf-grenoble.fr/ServiceObs/SiteWebAndes/
index.htm) and has been monitored continuously for more
than two decades. Available observations include topography (surface and bedrock), changes in surface elevation,
the spatial and temporal distribution of surface mass balance
and surface velocities.
All these observations are described in Section 2. The
model set-up, climate forcing and surface mass-balance
parameterization are detailed in Sections 3 and 4. Finally,
the calibration/validation of the model over the period
1997–2010 and projections for the 21st century are
described and discussed in Section 5.
2. STUDY AREA AND GLACIOLOGICAL DATA
Glaciar Zongo is located in the Bolivian Cordillera Real,
about 30 km from La Paz (Fig. 1). The glacier covers an area
of 1.9 km2 and flows on the southeastern side of the Huayna
Potosi summit from 6000 to 4900 m a.s.l. An extensive
network of glaciological, hydrological and meteorological
measurements on Glaciar Zongo has been developed since
1991, making it the glacier with the longest measurement
series in the tropics (Rabatel and others, 2013). The
observations used in this work to calibrate and validate
the glacier model include glacier topography (bedrock
topography and surface elevation), changes in surface
elevations, surface mass balances and surface velocities.
Digital elevation models (DEMs) at a resolution of 25 m
were computed from stereo-pairs of aerial photographs for
1997 and 2006 (Soruco and others, 2009), and allowed
accurate estimation of changes in the surface elevation over
the entire surface area of the glacier during the period
1997–2006. The limits of the glacier, and especially the
position of the front, were calculated using the same aerial
photographs and differential GPS measurements.
A surface DEM was used to calculate bedrock topography in ice-free areas. In the safely accessible parts of the
glacier, the ice thickness was measured in 2012 using icepenetrating radar (IPR). Our IPR is a geophysical instrument
specially designed by the Canadian company Blue System
Integration Ltd in collaboration with glaciologists to
measure the thickness of glacier ice (Mingo and Flowers,
2010). It comprises a pair of transmitting and receiving
10 MHz antennas that allow continuous acquisition, and is
Réveillet and others: Simulations of changes to Glaciar Zongo
Fig. 1. Glaciar Zongo, Bolivia. The inset map shows the location in
Bolivia. Glacier outlines in 1983, 1997 and 2006 are shown, as
well as the glaciological measurements network and the 2012 IPR
thickness profiles (adapted from Soruco and others, 2009).
georeferenced with a GPS receiver. Several profiles were
made on the glacier tongue, which revealed a maximum
thickness of 120 m at the foot of the seracs zone. Two
profiles made in the upper part of the glacier showed a
maximum thickness of 70 m (Fig. 1). In the seracs zone and
in the highly crevassed upper reaches of the glacier, ice
thickness was estimated taking into account the surface
slope of the glacier and checking for overall agreement
with the closest radar measurements taken above and
below the seracs zone.
The surface mass balance of Glaciar Zongo has been
measured since September 1991 using the glaciological
method (Rabatel and others, 2012). The annual mass
balance was obtained from measurements made at
21 stakes in the ablation area and in three snow pits/cores
located in the accumulation area (Fig. 1). Because of the
inaccessibility of some areas, including the steep seracs
zone in the middle of the glacier, which represents about
one-third of the glacier area, measurements cannot be made
over the entire glacier surface. For the period 1997–2006,
the annual mass-balance time series obtained using the
glaciological method was compared and calibrated against
the mass balance computed from the surface DEMs using
the geodetic method (Soruco and others, 2009).
Velocities were measured on the network of stakes
located in the ablation zone of the glacier (below
5200 m a.s.l.). Mean annual surface velocities measured at
each stake were computed from the position of the stakes
that have been measured precisely every year since 1991
using geodetic techniques (i.e. theodolite or differential
GPS). In the upper and middle parts of the glacier, the flow
was estimated using the movements of crevasses and seracs,
which are easy to identify on high-resolution satellite
images. This method is less accurate than geodetic surveys
(accuracy in meters rather than in centimeters) but is
sufficient in our particular case, as in these inaccessible
areas the surface velocities are between 40 and 50 m a–1.
Réveillet and others: Simulations of changes to Glaciar Zongo
91
strain-rate tensor D:
3. ICE FLOW MODEL
Glaciar Zongo flow dynamics were modeled using the
parallel finite-element model Elmer/Ice (Gagliardini and
others, 2013). This model was originally designed to solve
complex ice-flow problems for ice sheets and has since
been applied to model mountain glacier flow in several
studies (e.g. Zwinger and others, 2007; Jay-Allemand and
others, 2011; Adhikari and Marshall, 2013; Zhao and
others, 2014).
3.1. Mesh
Because of the small aspect ratio of the glacier, the threedimensional (3-D) mesh was constructed in two steps. First
we meshed a two-dimensional (2-D) footprint of our
domain. In all the simulations, the horizontal position of
our mesh nodes was fixed. As a consequence, in the upper
part of the glacier, where fluctuations in the margins of
the glacier are not expected, the model domain is given by
the glacier margin measured in 1997. In the lower part of the
glacier, the model domain was extended onto the glacier
foreland to allow the glacier to advance freely. This footprint
was meshed with unstructured triangular elements at a
spatial resolution of �25 m. This choice was a compromise
between spatial resolution and computational cost. The 2-D
mesh was then extruded vertically using six layers between
the bedrock and the free surface. The vertical resolution of
the bottom layer was set at approximately half the resolution
of the top layer to better resolve vertical gradients near the
bedrock. The resulting 3-D mesh contained 32 784 nodes.
The free surface elevation at the mesh nodes was
obtained from a cubic spline interpolation (Haber and
others, 2001) of the 1997 surface DEM. Owing to the lack of
bedrock-elevation measurements for some parts of the
glacier, bedrock elevation at the mesh nodes was obtained
using natural-neighbor interpolation (Fan and others, 2005).
3.2. Field equations
The 3-D velocity field u = (ux, uy, uz) is the solution of the
Stokes equations that expresses conservation of momentum
(Eqn (1)) and the conservation of mass in an incompressible
fluid (Eqn (2)):
r�
rP
�g ¼ 0
ru ¼ 0
ð1Þ
ð2Þ
where � is the deviatoric stress tensor, P is the isotropic
pressure, g = (0, 0, –9.81 m s–2) is the gravity vector and
� = 917 kg m–3 is the density of the ice. We ignored
variations in firn density in the accumulation area; this
assumption is discussed in Section 5.3.
The glacier-free surface zs (m) evolves with time
following the kinematic equation
@zs
@zs
@zs
þ ux
þ uy
@t
@x
@y
uz ¼ b
ð3Þ
where b (m w.e.) is the surface mass balance. As the finiteelement mesh cannot have a null thickness, a lower limit of
2 m above the bedrock elevation was applied to zs in
Eqn (3).
3.3. Ice-flow law
We used a viscous isotropic nonlinear flow law, Glen’s law
(Glen, 1955), to link the deviatoric stress tensor � to the
� ¼ 2�D
ð4Þ
The ice effective viscosity � in Eqn (4) is given by
� ¼ 12A
1=n
Dð1
e
nÞ=n
ð5Þ
where n is the Glen exponent, De ¼ 12trðD2 Þ is the second
invariant of the strain-rate tensor and A is a rheological
parameter that depends on temperature T following an
Arrhenius law:
A ¼ A0 e
Q=RT
ð6Þ
–1
where the activation energy Q is equal to 139 kJ mol , the
gas constant R is equal to 8.314 J K–1 mol–1 and the rate factor
A0 is equal to 1.916 103 Pa–3 s–1. Temperature measurements
in an ice core drilled at 6300 m a.s.l. in the accumulation
area of nearby Glaciar Illimani revealed a vertical temperature gradient in the ice and firn of �1°C (100 m)–1 (Gilbert
and others, 2010). For the sake of simplicity, given the
limited thickness of Glaciar Zongo, we ignored the variation
in temperature with depth and assumed that the temperature
inside the glacier is equal to the surface temperature. The
surface temperature was estimated from the mean air
temperature measured at a meteorological station located
at 5150 m a.s.l. on the glacier itself. We used a lapse rate of
–0.55°C (100 m)–1 (Sicart and others, 2011) to account for
the altitude effect. The glacier temperature was limited to a
maximum of 0°C, as the estimated mean air temperature can
be positive on the lowest part of the glacier. This temperature distribution was kept constant in all the simulations;
these assumptions are discussed in Section 5.3.
3.4. Boundary conditions
As the lower part of the glacier is temperate (Francou and
others, 1995), a certain amount of sliding of the ice on its
bed is to be expected. A linear friction law relating the basal
shear stress �b to the basal velocity ub was applied on the
lower boundary:
�b ¼ �ub
ð7Þ
The basal friction parameter � was adjusted by comparing
modeled and observed surface velocities. Because of the
scarcity of observations, we used a simple approach to
quantify it by trying to reproduce the observed surface flow
velocities. � was parameterized as a function of the bedrock
elevation, zb, only. For the highest part of the glacier
(z > 5600 m a.s.l.), where not much basal sliding was
expected, a constant value of 0.1 MPa was imposed for �.
For the lower part, an initial guess, � ini, was taken from
simple approximations: according to the shallow-ice approximation (Greve and Blatter, 2009) the basal shear stress
in Eqn (7) is computed as
�b ¼ �gh�
ð8Þ
where h is the thickness of the ice and � is the surface slope.
Following Eqn (7), we can then estimate �ini as
�b
�ini ¼
ð9Þ
ub
where ub is assumed to be the surface velocity measured at
the stake. � ini was set for the 12 elevation bands using the
mean values obtained from Eqn (9) and then linearly
interpolated at each mesh node. The mean differences
between modeled and observed velocities at each stake
from 1997 to 2006 are given for each elevation band in
92
Réveillet and others: Simulations of changes to Glaciar Zongo
Fig. 2. (a) Polynomial mass-balance function (dashed blue line) computed from 1997–2006 surface mass-balance measurements (the black
dots show the average mass balance for the period 1997–2006 for each elevation band, and blue shading shows the standard deviation).
(b) Mean surface velocities measured over the period 1997–2010 plotted against modeled velocities computed with � adjusted for the six
elevation bands given in Table 1. Blue error bars represent spatial and temporal variability of velocity measurements. Red error bars
correspond to spatial variability of simulated velocities.
Table 1 (note that the accuracy of velocity measurements
made using a differential GPS is a few centimeters). These
differences ranged from 7 to 13 m a–1, which was more than
the measured velocities. To reduce these differences and
obtain a better match between observed and modeled
velocities, the friction parameter was manually adjusted
using a trial-and-error method. The differences in surface
flow velocities obtained with this adjusted friction parameter
are listed in Table 1. These differences are lower than the
values obtained with the initial distribution of the friction
parameter (Fig. 2). The adjusted distribution of the friction
parameter was kept constant in both current and future
simulations. This assumption is discussed in Section 5.3.
For the lateral sides of the domain, two kinds of boundary
conditions were applied: in the upper part, where the glacier
extent is not expected to change, a null velocity was
applied; in the lower part, a stress-free condition was
applied as the model domain was extended compared with
the margins of the glacier in 1997; this condition was also
applied to non-glacierized areas and did not influence the
results. The limit between the two parts is located at the
average equilibrium-line altitude (ELA) in the period 1997–
2006, i.e. 5300 m a.s.l.
simulations due to uncertainties in the initial model
conditions (Seroussi and others, 2011). For that reason, we
allowed a relaxation of the free surface before all prognostic
simulations, in the same way that Gillet-Chaulet and others
(2012) had done. The length of the relaxation was a compromise between leaving sufficient time to remove the largest
transient effects but not too long, so that the free surface
remains close to observations. We chose a relaxation period
of 8 years. The surface mass balance b in Eqn (3) was kept
constant over the relaxation period and was given by
observations made in 1995. We chose these observations
because the mass balance integrated over the whole glacier
surface was nearly zero, resulting in only small changes in
the glacier total volume during the relaxation period.
The glacier geometry at the end of the relaxation period
was compared with the observed glacier geometry in 1997
(Fig. 3). The difference between the modeled and measured
glacier areas was <1%. Changes in glacier thickness
between the beginning and the end of the relaxation period
were �1 m in the lower part and <5 m in the upper part.
3.5. Relaxation
4. CLIMATE FORCING AND MASS-BALANCE
PARAMETERIZATION
4.1. Climate forcing for the 21st century
It is well known that changes in surface elevation show high
and unphysical values at the beginning of prognostic
Temperatures were taken from the CMIP5 results to force the
relationship between temperature and the ELA used to
Table 1. Differences between modeled and observed surface velocities (m a–1) averaged for each elevation band, with the initial friction
parameter distribution �ini (Eqn (9)) and the adjusted friction parameter
Altitude
range
Number of
measurements
m a.s.l.
4900–4970
4970–5030
5030–5070
5070–5160
5160–5250
5250–5300
17
15
31
87
31
11
Initial friction
parameter � ini
Difference between modeled and
observed surface velocities with �ini
Adjusted friction
Difference between modeled and
parameter �
observed surface velocities with �adjusted
MPa a m–1
m a–1
MPa a m–1
m a–1
0.0023
0.0071
0.0066
0.0053
0.011
0.0057
–11.0
9.6
7.6
–9.9
7.3
12.9
0.0033
0.0050
0.0045
0.0058
0.0070
0.0040
–5.4
2.1
0.7
–2.6
1.1
–0.03
Réveillet and others: Simulations of changes to Glaciar Zongo
93
Fig. 3. Simulated thickness of Glaciar Zongo in 1997, 2006 and 2010. The glacier outline observed in 1997 is represented by a dotted line in
each diagram. The front position observed in 2006 and 2010 is represented by bold lines.
quantify the surface annual mass-balance distribution over
the 21st century. We selected nine global climate models
and three representative concentration pathways (RCPs).
Scenarios RCP2.6, RCP6.0 and RCP8.5 are based on
radiative forcing of 2.6 W m–2, 6.0 W m–2 and 8.5 W m–2,
respectively. Scenario RCP2.6 is the most optimistic scenario in terms of greenhouse gas emissions, while scenario
RCP8.5 is the most pessimistic. Scenario RCP6.0 is considered intermediate. For each of the nine climate models
used, we considered the modeled annual average 2 m
air temperature for the 21st century for the coordinates
15–18° S, 68–70° W, which cover the location of Glaciar
Zongo. The modeled temperature data were converted into
anomalies by subtracting the 1997–2006 average.
4.2. Mass-balance parameterization
For the calibration/validation period, the annual surface
mass balance was derived from observations in 12 elevation
bands from 4900 to 6000 m a.s.l.
For the future simulations, we proceeded in two steps:
First, the vertical profile of surface mass balance computed from the available annual measurements averaged
over the period 1997–2006 was fitted by a polynomial
function to obtain a mass-balance function (Fig. 2a); this
function gave a better representation of the observed
data. Note that this function has been used for the
validation period to test its efficiency compared with the
use of direct surface annual mass-balance measurements,
giving similar results.
Second, we combined the ELA sensitivity to temperature
with the temperature anomalies given by the climate
models (Section 4.1) to obtain a projection of the annual
ELA for the 21st century. Note that the sensitivity of
Glaciar Zongo ELA to temperature was estimated by
Lejeune (2009) to be 150 � 30 m °C–1. To link changes in
ELA to changes in the spatial mass-balance distribution
over the glacier surface, we assumed that the relationship based on the measurement period will continue
over the 21st century. Then the mass-balance function
was shifted according to the annual position of the ELA
to obtain the annual spatial mass-balance distribution for
all elevations of the glacier surface. Note that the
changes in surface area and surface elevation of the
glacier are taken into consideration for future simulations
because the mass balance was computed for each point
of the mesh at each time step and both the glacier
surface area and the glacier surface elevation were
updated at each time step.
5. RESULTS AND DISCUSSION
5.1. Recent period (1997–2010)
Prognostic simulations were run for the period 1997–2010.
Two independent datasets based on field measurements
were used to constrain and validate the model. First, the
model was forced and calibrated with available observations of topography, surface velocities and surface mass
balance. The adjusted values of the basal friction parameter
led to simulated surface velocities close to the field
measurements (see Section 3.4). Then the model was
validated over the recent period using different datasets
from those used for calibration: the position of the front and
the total volume loss.
Observed and modeled glacier outlines in 2006 and 2010
are compared in Figure 3. The retreat of the glacier front
between 1997 and 2010 was well reproduced by the model.
The difference between the simulated and measured glacierized areas was <1.5% in 2006 and <1% in 2010. The
observed retreat of the front was 140 m between 1997 and
2006 and 50 m between 2006 and 2010. Results of the
simulations were 125 m and 60 m, respectively. Modeled
changes in surface elevation between 1997 and 2006 are
shown in Figure 4 and compared with the measurements
obtained by photogrammetry (Soruco and others, 2009).
Measurements revealed a maximum shift from �40 m for
the glacier tongue down to �15 m below the seracs zone.
These model results are in good agreement in terms of both
spatial distribution and magnitude. Indeed, the volume loss
computed by photogrammetry was 1.10 � 107 m3 while the
simulated volume loss was 0.95 � 107 m3. This 13% difference in volume loss is within the range of accuracy of the
photogrammetric method.
5.2. Simulations of the 21st century
Simulations of the 21st century started in 2006. The state of
the glacier in 2006 was projected by the simulations
covering the calibration period (1997–2006), described in
Section 5.1.
Volume projections for Glaciar Zongo with temperature
anomalies obtained from the nine climate models for
94
Réveillet and others: Simulations of changes to Glaciar Zongo
Fig. 4. Changes in surface elevation between 1997 and 2006: (a) simulated by the model, (b) measured by photogrammetry (adapted from
Soruco and others, 2009). (c) Difference between absolute model and observed surface elevation changes.
scenario RCP2.6 and for a sensitivity of the ELA of
150 m °C–1 are shown in Figure 5. All model results showed
similar trends, with a continuous decrease in glacier volume
down to �50% of its present value, until the period 2035–
60, followed by stabilization of the volume of the glacier
until the end of the century. This stabilization reflects the
temperature stabilization projected by the models with a
time lag of about 10–15 years. The scatter of the volumes
projected by the nine models is large and increases with
time, with cumulative volume losses of 11–39% in 2030,
18–48% in 2050 and 32–59% in 2100.
Volume changes computed using temperature data from
the three RCP scenarios are shown in Figure 6. The solid
lines show the average of the nine-model forcing, and the
shaded area shows the 1� interval, where � is the standard
deviation of the nine model outputs. The three scenarios
projected similar continuous mass loss until approximately
2035. As already mentioned, the change in volume
projected by scenario RCP2.6 then remained stable for the
rest of the century, whereas the two other scenarios
projected a continuous decrease until the end of the
century. As expected, RCP8.5 projected the highest rate of
volume loss, with the glacier nearly disappearing in 2100.
The volume losses projected by scenarios RCP2.6, RCP6.0
and RCP8.5 were respectively 27 � 7%, 24 � 7% and
29 � 8% in 2030; 35 � 8%, 34 � 7% and 44 � 7% in
2050; and 40 � 7%, 69 � 7% and 89 � 4% in 2100.
Lastly, we assessed the sensitivity of the volume changes
computed by the model considering the sensitivity of the ELA
to temperature changes. The average changes in volume
obtained with the three RCP scenarios for ELA sensitivities to
temperature of +120 m °C–1, +150 m °C–1 and +180 m °C–1
are shown in Figure 7. As expected, the trends are similar and
the volume loss increased with an increase in the sensitivity
of the ELA. The average volume losses in 2100 obtained with
the three values of the sensitivity were respectively 35%,
Fig. 5. (a) Simulated Glaciar Zongo volumes from 1997 to 2100 using the RCP2.6 scenario. Results are given for the nine climate models
used in this study and an ELA sensitivity of 150 m °C–1. The horizontal dashed line indicates half the 2006 volume of Glaciar Zongo.
(b) Temperature anomalies (compared with the 1997–2006 period) from 2006 to 2100 projected using the RCP2.6 scenario and the nine
CMIP5 models.
Réveillet and others: Simulations of changes to Glaciar Zongo
95
Fig. 6. Simulated Glaciar Zongo volumes from 1997 to 2100 using
scenarios RCP2.6 (purple), RCP6.0 (green) and RCP8.5 (orange).
Solid lines show the average of the nine models, and the shaded
area shows the �1� interval. The horizontal dashed line indicates
half the current volume of Glaciar Zongo.
Fig. 7. Simulated Glaciar Zongo volumes from 1997 to 2100 using
scenarios RCP2.6 (purple), RCP6.0 (green) and RCP8.5 (orange).
Solid lines represent an ELA sensitivity of 150 m °C–1. Dashed lines
represent a sensitivity of 180 m °C–1 and 120 m °C–1. The horizontal
dashed line indicates half the current volume of Glaciar Zongo.
40%, 45% with RCP2.6; 60%, 69%, 77% with RCP6.0; and
82%, 89%, 94% with RCP8.5.
annual values for extreme positive/negative mass-balance
years. Impacts of this approach are hardly quantifiable at
secular scale, and in any case are assumed to be limited
compared with the large scatter of temperature changes
related to the different scenarios and climate models.
5.3. Limitations of our study
While this study is among the first to use a full-Stokes model
for a mountain glacier application, modeling ice dynamics
still relies on three main assumptions: (i) basal sliding is
parameterized using a linear friction law where the coefficient is a function of altitude only; (ii) the viscosity field
was calibrated from current observations of the surface air
temperature, and thermomechanical coupling is ignored;
(iii) our glacier is composed only of ice, and variations in
density are ignored.
Sensitivity tests for the first two assumptions were made
for the validation period (1997–2010, Section 5.1). Variations of �10% for the friction coefficient and the temperature led to variations in volume of <1% and <0.05%,
respectively, in 2010.
In the case of a mountain glacier with no calving front
and a surface mass balance parameterized as a function of
altitude only, ice dynamics affect glacier volume only by
altering the surface area of the glacier and free surface
elevation. This explains the low sensitivity of the variations
in volume to the ice dynamics parameters and justifies the
use of pragmatic assumptions. Progress is underway to
model these processes more accurately (e.g. Gilbert and
others, 2014), and these processes will be incorporated in
our simulations when the complexity of the coupling
between ice dynamics and surface mass balance requires it.
Finally, uncertainties in the simulations of glacier
changes for the coming decades mostly depend on climate
changes and their impact on the surface mass-balance
quantification. Our approach for surface mass-balance
parameterization is simple but relies on direct surface
mass-balance measurements. Using such a parameterization
together with ELA shifts for future simulations may lead to
uncertainties regarding interannual surface mass-balance
variations. As shown in Figure 2, temporal mass-balance
variability is higher in the lower reaches of the glacier than
in the upper ones. Consequently, assuming a linear shift of
the surface mass-balance profile leads to overestimated
6. CONCLUSION
This paper describes the first application of a 3-D full-Stokes
model on a mountain glacier in the tropical Andes to take
into account the ice dynamics in ongoing and future glacier
changes. Glaciar Zongo is a perfect candidate for such an
application because the glacier has been continuously
monitored since the early 1990s by the GLACIOCLIM
observatory, therefore all the data needed to calibrate and
validate the model are available. In simulating the future
mass balance, our approach was based on the sensitivity of
the ELA to temperature changes and assumed that the
observed vertical profile of surface mass balance remains
unchanged. Regarding glacier dynamics, some assumptions
were made concerning basal sliding, the internal temperature of the ice and the density of the material as their impact
is very limited in simulations of the glacier changes
compared with the impact of changes in climate conditions
and hence in the mass balance.
For the 1997–2010 validation period, the modeled
surface area and changes in volume were in good agreement
with observations. Consequently, the model was then used
to simulate future changes in Glaciar Zongo during the 21st
century using nine different climate models and three RCP
scenarios. In the near future (2030), the variability between
the different climate models was greater than the variability
between the scenarios, and the volume loss ranged from
24 � 7% to 29 � 8%. The changes in volume computed with
the three RCP scenarios differed significantly after 2050.
Scenario RCP2.6 projected a stable volume in the second
half of the century with a value corresponding to �60% of its
present volume, while the other two scenarios projected
continuous and sustained volume loss over the whole
century, with the near disappearance of the glacier projected
in 2100 by the most pessimistic scenario, RCP8.5.
96
Future research could focus on (1) simulations of massbalance changes using a complete surface energy-balance
model; (2) considering a certain amount of snow/firn with
different density values and rheological properties; (3) considering fracturing of the ice that would make it possible to
represent specific zones of glaciers, like the seracs zone.
ACKNOWLEDGEMENTS
This study was funded by the French Institut de Recherche
pour le Développement (IRD) through the Andean part of the
French glacier observatory service, GLACIOCLIM (http://
www-lgge.ujf-grenoble.fr/ServiceObs/SiteWebAndes/index.
htm), and was conducted in the framework of the International Joint Laboratory GREAT-ICE, a joint initiative of the
IRD and universities and institutions in Bolivia, Peru, Ecuador
and Colombia. Contributing authors from the Laboratoire de
Glaciologie et Géophysique de l’Environnement (LGGE)
acknowledge the contribution of LABEX OSUG@2020, ANR
grant No. ANR-10-LABX-56. We are grateful to all those who
took part in field campaigns for mass-balance measurements,
to Benjamin Lehmann (IRD) for his help with the radar field
campaign, to Gerhard Krinner (LGGE) for providing the
CMIP5 data for our region of interest, and to Laurent Mingo
(Blue Ice Integration Ltd) for assistance with the IPR (http://
www.radar.bluesystem.ca/). This work was granted access to
the high-performance computing resources of CINES under
the allocation 2014-016066 made by GENCI. Finally, we
thank G. Aðalgeirsdóttir (Scientific Editor) and two anonymous referees for constructive comments that helped to
improve the paper.
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